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  • A body covered a distance of 'x' meter along a semicircular path. calculate the magnitude of displacement of the body and the ratio of distance to displacement?

A body covered a distance of 'x' meter along a semicircular path. calculate the magnitude of displacement of the body and the ratio of distance to displacement?

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A body covered a distance of x meter along a semicircular path.

 

 

 

\\ The \ magnitude \ of \ the \ displacement \ of \ the \ body\ is,\ \\ \\ |s|=2 r \ldots \ldots \ldots \ldots \ldots \ldots(1) \\ since \ the \ distance \ traveled \ by \ the \ body \ is,\\ \begin{aligned} A B &=\pi r=x \\ r &=\frac{x}{\pi} \end{aligned} \\ Substitute \ this \ value \ in \ equation \ (1)\\ \\ \\ |s|=2 r=\frac{2 x}{\pi} \\ The \ ratio \ of \ the \ distance \ to \ displacement\ is,\ \\ R=\frac{x}{|s|}=\frac{x}{\frac{2 x}{\pi}}=\frac{\pi}{2} \\ Therefore, \ the \ magnitude \ of \ displacement \ is \ \frac{2 x}{\pi} \ and \ the \ value \ of \ ratio \ is \ \frac{\pi}{2}

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Deependra Verma

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